31 citations · 131 across the 24 of their papers we have counts for
6 papers · 1 filter
Unconditional Chebyshev biases in number fields
Daniel Fiorilli, Florent Jouve
Prime counting functions are believed to exhibit, in various contexts, discrepancies beyond what famous equidistribution results predict; this phenomenon is known as Chebyshev's bi…
Moments of moments of primes in arithmetic progressions
Régis de la Bretèche, Daniel Fiorilli
We establish unconditional -results for all weighted even moments of primes in arithmetic progressions. We also study the moments of these moments and establish lower bounds und…
On a conjecture of Montgomery and Soundararajan
Régis de la Bretèche, Daniel Fiorilli
We establish lower bounds for all weighted even moments of primes up to in intervals which are in agreement with a conjecture of Montgomery and Soundararajan. Our bounds hold u…
A disproof of Hooley's conjecture
Daniel Fiorilli, Greg Martin
Define to be the variance of primes in the arithmetic progressions modulo , weighted by . Hooley conjectured that as soon as tends to infinity and…
The first moment of primes in arithmetic progressions: Beyond the Siegel-Walfisz range
Sary Drappeau, Daniel Fiorilli
We investigate the first moment of primes in progressions as . We show unconditio…
Distribution of Frobenius elements in families of Galois extensions
Daniel Fiorilli, Florent Jouve
Given a Galois extension of number fields, we describe fine distribution properties of Frobenius elements via invariants from representations of finite Galois groups and rami…